Subgroups — C₂×C₁₃×C₁₉⋊(C₅²⋊C₃) #49150308

Order 37050.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉⋊(C₅²⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₃×C₁₉	—	3	2	no	—
6	C₂×C₁₃×C₅²⋊C₃	—	19	1	no	maximal, Hall
7	C₂×C₁₃×C₁₉⋊C₃	—	25	1	no	maximal, Hall
8	C₁₉⋊(C₅²⋊C₃)	C₂×C₁₃	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₁₃×C₁₉	—	3	2	no	—
10	C₁₃×C₅²⋊C₃	—	19	1	no	Hall
11	C₂×C₅²×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₁₉⋊C₃	—	25	1	no	Hall
13	C₂×C₅²×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₁₉	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
16	C₅²×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₁₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₁₉	—	3	2	no	—
19	C₂×C₅²⋊C₃	—	19	1	no	Hall
20	C₂×C₅×C₁₃	—	3	2	no	—
21	C₂×C₁₉⋊C₃	—	25	1	no	Hall
22	C₅×C₁₉	—	3	2	no	—
23	C₂×C₃×C₁₃	—	475	1	no	Hall
24	C₅²⋊C₃	—	19	1	no	Hall
25	C₅×C₁₃	—	3	2	no	—
26	C₁₉⋊C₃	—	25	1	no	Hall
27	C₂×C₅²	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₃×C₁₃	—	475	1	no	Hall
29	C₂×C₁₉	C₁₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₁₃	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Hall
31	C₅²	C₂×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₁₉	C₂×C₁₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₁₃	C₂×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×C₅	—	3	2	no	—
35	C₂×C₃	—	475	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	475	1	no	Sylow
38	C₂	C₁₃×C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₁₉⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₃×C₁₉	C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₁₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×C₁₉⋊(C₅²⋊C₃)	C₂	direct (N × H)
2. C₂×C₅²×C₁₃×C₁₉	C₃	semidirect
3. C₅²×C₁₃×C₁₉	C₂×C₃	semidirect
4. C₂×C₁₉⋊(C₅²⋊C₃)	C₁₃	direct (N × H)
8. C₁₉⋊(C₅²⋊C₃)	C₂×C₁₃	direct (N × H)
11. C₂×C₅²×C₁₉	C₃×C₁₃	semidirect
13. C₂×C₅²×C₁₃	C₁₉⋊C₃	semidirect
14. C₂×C₁₃×C₁₉	C₅²⋊C₃	semidirect
15. C₅²×C₁₉	C₂×C₃×C₁₃	semidirect
16. C₅²×C₁₃	C₂×C₁₉⋊C₃	semidirect
17. C₁₃×C₁₉	C₂×C₅²⋊C₃	semidirect
27. C₂×C₅²	C₁₃×C₁₉⋊C₃	semidirect
29. C₂×C₁₉	C₁₃×C₅²⋊C₃	semidirect
30. C₂×C₁₃	C₁₉⋊(C₅²⋊C₃)	direct (N × H)
31. C₅²	C₂×C₁₃×C₁₉⋊C₃	semidirect
32. C₁₉	C₂×C₁₃×C₅²⋊C₃	semidirect
33. C₁₃	C₂×C₁₉⋊(C₅²⋊C₃)	direct (N × H)
38. C₂	C₁₃×C₁₉⋊(C₅²⋊C₃)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×C₁₉⋊(C₅²⋊C₃)	2
C₂×C₅²×C₁₃×C₁₉	3
C₂×C₁₉⋊(C₅²⋊C₃)	13
C₂×C₁₃×C₅²⋊C₃	19
C₂×C₁₃×C₁₉⋊C₃	25

Subgroups — C2×C13×C19⋊(C52⋊C3) #49150308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₁₉⋊(C₅²⋊C₃) #49150308